Relativistic electron beams above thunderclouds

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ACPD

11, 15551–15572, 2011

Relativistic electron beams

M. F ¨ullekrug et al.

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Atmos. Chem. Phys. Discuss., 11, 15551–15572, 2011 www.atmos-chem-phys-discuss.net/11/15551/2011/ doi:10.5194/acpd-11-15551-2011

Atmospheric Chemistry and Physics Discussions

This discussion paper is/has been under review for the journal Atmospheric Chemistry and Physics (ACP). Please refer to the corresponding final paper in ACP if available.

Relativistic electron beams above

thunderclouds

M. F ¨ullekrug1, R. Roussel-Dupr ´e2, E. M. D. Symbalisty3, J. J. Colman4,

O. Chanrion5, S. Soula6, O. van der Velde7, A. Odzimek8, A. J. Bennett9,

V. P. Pasko10, and T. Neubert5

1

University of Bath, Centre for Space and Atmospheric Research, Department of Electronic and Electrical Engineering, Bath, UK

2

SciTech Solutions, Melbourne, Florida, USA 3

Atmospheric, Earth and Environment Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico, USA

4

Kirtland Airforce Base, USAF AFMC AFRL/RVBXP, New Mexico, USA 5

National Space Institute, Technical University of Denmark, Copenhagen, Denmark 6

Laboratoire d’A ´erologie, Universit ´e de Toulouse, Toulouse, France. 7

Department of Electrical Engineering, Universitat Polit `ecnica de Catalunya, Terrassa, Spain 8

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Passive Sensing, Met Office, Exeter, UK

10

Department of Electrical Engineering, Pennsylvania State University, Pennsylvania, USA

Received: 25 April 2011 – Accepted: 18 May 2011 – Published: 20 May 2011

Correspondence to: M. F ¨ullekrug ([email protected])

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Abstract

Non-luminous relativistic electron beams above thunderclouds are detected by radio remote sensing with low frequency radio signals from ∼40–400 kHz. The electron beams occur∼2–9 ms after positive cloud-to-ground lightning discharges at heights be-tween∼22–72 km above thunderclouds. The positive lightning discharges also cause 5

sprites which occur either above or before the electron beam. One electron beam was detected without any luminous sprite occurrence which suggests that electron beams may also occur independently. Numerical simulations show that the beamed electrons partially discharge the lightning electric field above thunderclouds and thereby gain a mean energy of ∼7 MeV to transport a total charge of ∼10 mC upwards. The impul-10

sive current associated with relativistic electron beams above thunderclouds is directed downwards and needs to be considered as a novel element of the global atmospheric electric circuit.

1 Introduction

Sprites (Neubert et al., 2008; F ¨ullekrug et al., 2006; Rakov and Uman, 2003; Sentman 15

et al., 1995; Franz et al., 1990) and gigantic jets (Cummer et al., 2009; Su et al., 2003; Pasko et al., 2002) are luminous streamer (Luque and Ebert, 2009; Pasko et al., 1998) and leader (Riousset et al., 2010; Krehbiel et al., 2008; Pasko and George, 2002) dis-charges resulting from conventional breakdown in the middle atmosphere. Sprites may also be associated with electron beams resulting from relativistic runaway breakdown 20

within or above thunderclouds (Østgaard et al., 2008; Inan, 2005; Smith et al., 2005; Roussel-Dupr ´e and Gurevich, 1996; Fishman et al., 1994). The newly-recognised run-away breakdown mechanism (Gurevich and Zybin, 2005; Gurevich et al., 1992) inside thunderclouds (Shao et al., 2010; Dwyer et al., 2009) can initiate at∼1/10 of the con-ventional breakdown electric field threshold (Marshall et al., 1995) and requires a pop-25

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11, 15551–15572, 2011

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electron avalanche growth (Gurevich et al., 2003). The population of seed particles must be above the runaway threshold of∼10 keV or more, depending on the strength of the electric field, and could originate from ∼1015–1016eV cosmic rays (Gurevich et al., 2009; Gurevich and Zybin, 2005) or thermal runaway in leader and/or streamer tips (Celestin and Pasko, 2011; Colman et al., 2010; Moss et al., 2006). The runaway 5

avalanche can result in a population of electrons with energies as high as tens of MeV inside the thundercloud (Shao et al., 2010; Dwyer et al., 2009; Gurevich et al., 1992). Whether relativistic electron beams can also occur above thunderclouds is currently not known (Østgaard et al., 2008; Inan, 2005; Smith et al., 2005; Roussel-Dupr ´e and Gure-vich, 1996; Fishman et al., 1994) even though narrow beams of relativistic electrons 10

are now routinely observed in space (Briggs et al., 2011; Cohen et al., 2010; Carlson et al., 2009; Dwyer et al., 2008). Relativistic electron beams are occasionally associ-ated with sprites as inferred from radio remote sensing with low frequency radio signals from∼40–400 kHz (F ¨ullekrug et al., 2010). These radio signals are analyzed here in detail to determine the height of relativistic electron beams above thunderclouds and 15

to determine the associated charge transfer through the middle atmosphere.

2 The mesocale convective system, lightning discharges and sprites

Thunderstorms and lightning activity in southern Europe have recently attracted special interest because numerous sprites are observed with video cameras above thunder-clouds which regularly develop during the summer months from the beginning of May 20

to mid-September (Soula et al., 2009; Neubert et al., 2008). For example, several thundercloud cells initiated over the Bay of Biscay and northern Spain in the late af-ternoon on 30 August 2008. The thunderstorms migrated northward through France and merged to an exceptional mesoscale convective system during the night until it decayed away in the late morning hours when reaching the English Channel which 25

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brightness temperature recorded on board the Meteosat Second Generation (MSG) satellite at 01:45 UTC (Fig. 1). The convective core of the thunderstorm reached a height of ∼12 km with cloud top temperatures as cold as ∼−64 C◦_{. Many negative}

lightning discharges cluster in the convective core which is surrounded by some posi-tive lightning discharges reported by the French lightning detection system M ´et ´eorage 5

at the time when Meteosat scanned the electrified thundercloud from 01:50 UTC to 02:00 UTC.

One particular positive lightning discharge at 01:52:59.524 UTC (46.54◦_{N, 0.48}◦_E)

with a peak current of ∼47.1 kA causes a sprite discharge above the thundercloud (Fig. 2) which is observed with a video camera located on the top of Pic du Midi in the 10

French Pyr ´en ´ees (42.93◦_{N, 0.14}◦_{E, 2877 m elev.) and another video camera located in}

Sant Vicenc¸ de Castellet in North-Eastern Spain (41.67◦_{N, 1.86}◦_{E, 193 m elev.). The}

sprite discharge consists of the main body of the sprite surrounded by three columni-form sprites at distances up to∼20 km. The main body of the sprite extends upwards from∼60 km to∼85 km height as triangulated by use of the two video cameras. The 15

sprite tendrils extend downwards from∼60 km to∼50 km below the main body of the sprite.

The sprite luminosity curve is delayed by∼3–6 ms with respect to the causative pos-itive lightning discharge (Fig. 3) as evidenced by high speed (20 kHz) recordings with a photometer located at Pic du Midi and vertical electric field recordings with a wide-20

band digital radio receiver (F ¨ullekrug, 2010) located near Bath in South-West England of the United Kingdom (51.35◦_{N, 2.29}◦_{W). The sprite causing positive cloud-to-ground}

lightning discharge causes a strong burst of electromagnetic radiation which spans the entire frequency range of the radio receiver. A large fraction of this electromagnetic energy is deposited in the narrow frequency range from∼5-16 kHz which is typical for 25

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11, 15551–15572, 2011

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range from∼5–16 kHz which is untypical for conventional lightning discharges. The first radiation burst coincides with the sprite luminosity and the second radiation burst shortly follows the sprite luminosity. Both radiation bursts are thought to be caused by electron beams above the thundercloud resulting from relativistic runaway breakdown (F ¨ullekrug et al., 2010).

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3 Relativistic electron beams

Seven similar untypical broadband bursts of electromagnetic radiation following sprite producing lightning discharges have been collected during sprite observations in the years 2008 and 2009 (Table 1). In these two years, a total of ∼140 sprite observa-tions have been examined such that the occurrence rate of the electromagnetic radi-10

ation bursts is ∼5 %. These bursts all occured ∼2–9 ms after sprite causing positive cloud-to-ground lightning discharges. The average spectrum of the seven bursts is rel-atively flat at frequencies<40 kHz when compared to the average spectrum of their parent lightning discharges (Fig. 4, left). This is consistent with simulations of vir-gin air high frequency breakdown. The spectral amplitudes of the broadband electro-15

magnetic radiation bursts are as small as∼100 µ Vm−1Hz−1/2 in the frequency range from∼40-400 kHz, but still∼1–2 orders of magnitude above an average background spectrum which is recorded 10 ms prior to the causative lightning discharges for ref-erence (Fig. 4, left). This background spectrum exceeds the ultimate sensitivity limit of the wideband digital radio receiver∼1–2 µVm−1Hz−1/2 by ∼1 order of magnitude 20

(Fig. 4, right). Superimposed on the sensitivity limit of the receiver are the omni-present low-frequency, or long-wave, radio transmitters in this frequency range, e.g., the United Kingdom radio clock at 60 kHz (the former Rugby MSF signal, now transmit-ted from Anthorn), France Inter at 162 kHz, Europe 1 at 183 kHz, and BBC radio 4 at 198 kHz. These radio transmitters have a typical narrow bandwidth of∼10–12 kHz and 25

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11, 15551–15572, 2011

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Numerical simulations of relativistic electron beams above thunderclouds predict the-oretically broadband bursts of electromagnetic radiation with a flat spectrum following sprite producing lightning discharges (F ¨ullekrug et al., 2010) in agreement with our experimental observations. These model calculations solve kinetic particle equations on the microscopic scale and Maxwell’s equations on the macroscopic scale simulta-5

neously. The causative lightning continuing current drains charge from the thunder-cloud which exposes the area above the thunderthunder-cloud to a quasi-static electric field. When this electric field exceeds the runaway breakdown threshold and a coinciding stratospheric cosmic ray shower (Roussel-Dupr ´e et al., 1998) produces sufficient ener-getic seed electrons, an electron avalanche above the thundercloud is initiated which 10

quickly develops into an upward propagating relativistic electron beam. The beamed electrons partially discharge the lightning electric field and thereby gain a mean energy of∼7 MeV with a spread of ∼6 MeV while carrying a total charge of∼10 mC upward as inferred from the comparison between the measured and simulated electron beam spectrum (Fig. 4, left and right). Impulsive changes of this downward current from the 15

electron beam result in the observed bursts of electromagnetic radiation a few ms after the causative lightning discharge.

The initial lightning discharge and the subsequent electron beam launch electromag-netic waves which can propagate on several paths from the source location to the radio receiver. These propagation paths can be inferred from a detailed analysis of the ob-20

served electromagnetic radiation bursts. The burst of electromagnetic radiation from the lightning discharge is composed of two consecutive pulses which are delayed by ∼102 µs (Fig. 5, upper panel). The first pulse results from the electromagnetic wave which propagates from the lightning discharge to the receiver along the surface of the Earth and is denoted ground wave. The second pulse results from the electro-25

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11, 15551–15572, 2011

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wave propagation simulations with Finite-Difference-Time-Domain (FDTD) modeling. Electromagnetic waves with two or more ionospheric reflections are more strongly at-tenuated and they are not detected above the background level of the interfering radio transmitters.

The burst of electromagnetic radiation from the electron beam at ∼4.4 ms is also 5

composed of two consecutive pulses which are delayed by∼59 µs (Fig. 5, lower panel). The first pulse results from the direct wave which propagates at an angle to the receiver and is denoted direct wave. The second pulse results from the electromagnetic wave which is reflected from the ionosphere and is denoted sky wave. The time delay be-tween the direct wave and the sky wave determines the height of the electron beam 10

to be∼41 km for the known ionospheric height of∼90 km (Fig. 6). The electron beam is therefore located well above the thundercloud which terminates at an altitude of ∼12 km. The burst of electromagnetic radiation at∼8.9 ms emanates from a height of ∼72 km and could result from the same electron beam or another independent second electron beam. If the observed radiation burst is interpreted to emanate from the same 15

electron beam, the beam would propagate with an average velocity of ∼7000 km/s through the middle atmosphere as inferred from the difference between the two emis-sion heights∼31 km and the corresponding time delay∼4 ms. The heights of two more electron beams associated with other sprite discharges during the same night are de-termined to be∼16 km and∼22 km, both of which are well above the thundercloud. 20

4 Discussion

A sensitivity analysis of the height determination methodology reveals that a variation of the observed time delay by∼1 µs corresponds to a ∼1 km vertical height variation such that the height of the electron beam can be determined in a very accurate way. If the observed time delay is interpreted as a variation in the distance between the source 25

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sensitivity analysis was performed to determine the optimum distance between the lightning discharge and the radio receiver which maximizes the signals of the ground and sky wave. This distance was found to be ∼300–400 km such that at larger dis-tances, it becomes increasingly difficult to distinguish the ground and sky wave from the background noise of the interfering radio transmitters. Finally, all lightning discharges 5

with a peak currentI_p

>30 kA reported by M ´et ´eorage from 00:00–04:00 UTC on 31

August 2008, have been investigated. Only one additional electromagnetic radiation burst with a flat spectrum from ∼40-400 kHz could be found which is similar to the three examples reported here. The burst follows ∼5 ms after two consecutive posi-tive lightning discharges at 01:29:09.785 and .786 UTC. This singular observation is 10

indicative of a non-luminous relativistic electron beam without any sprite occurrence as evidenced by the two video cameras. The preliminary result suggests that lightning discharges may also cause relativistic electron beams above thunderclouds without producing sprites because the relativistic breakdown threshold is only ∼1/10 of the conventional breakdown threshold. It is also possible that the observed electromag-15

netic radiation bursts are related to secondary sprite processes sometimes observed above thundercloud tops (Pasko, 2010; Marshall and Inan, 2007; Moudry, 2003). How-ever, these processes remained sub-visual in the optical observations reported in this work, and it is not clear why such a hypothetical process would emit low frequency electromagnetic radiation while the sprite itself does not. It is interesting to note that 20

the low frequency electromagnetic radiation reported here can be observed in space as a result of its transionospheric propagation (F ¨ullekrug et al., 2011, 2009) and it may be associated with high frequency electromagnetic radiation (Parrot et al., 2008).

5 Summary

In summary, relativistic electron beams above thunderclouds have been detected si-25

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11, 15551–15572, 2011

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Both results suggest that non-luminous electron beams and luminous sprites indepen-dently discharge lightning electric fields in the middle atmosphere. The observed rel-ativistic electron beams above thunderclouds occur simultaneously with ∼5 % of all optically observed sprites and they are thus very rare. The small number of pho-tons possibly emanating from non-luminous relativistic electron beams and sub-visual 5

streamers may be identified in future studies by combining more sensitive optical ob-servations with interferometric radio recordings to map the low-frequency radio sky above thunderclouds. However, the relativistic electron beams are a new form of im-pulsive energy transfer between thunderclouds and the middle atmosphere which need to be considered as a novel element in the global atmospheric electric circuit (Rycroft 10

and Odzimek, 2010; Rycroft, 2006; Rycroft et al., 2000).

6 Methods

The Meteosat Second Generation satellite measures the thermal infrared radiation of the Earth from 10.5-12.5µm with a Ritchey-Chr ´etien telescope connected to a HgCdTe detector. This passive imaging radiometer is calibrated with two black bodies at 290 K 15

and 340 K and it scans the full Earth disk every 15 minutes. The optical camera system on Pic du Midi consists of a wide-angle, low-light, video camera and a high-speed pho-tometer mounted on a pan-tilt unit. The camera is equipped with a 16 mm, f 1.40 lens with a field of view of 31◦_{and it has an exposure time of 40 ms for one image. The}

pho-tometer counts photon emissions at a sampling rate of 20 kHz with a time resolution of 20

50 ms. The camera system is synchronized to UTC with a Global Positioning Satellite (GPS) receiver with an absolute timing accuracy <1 ms. The optical camera system in Sant Vicenc¸ de Castellet is a Watec 902H2 equipped with a 12 mm, f 0.8 lens with a field of view of 31◦ _{and an exposure time of 20 ms. The French lightning detection}

system M ´et ´eorage covers southwestern Europe and the western Mediterranean Sea. 25

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<4 km, and timing accuracy<1 ms. The wideband digital radio receiver near Bath in the UK measures the vertical electric field strength by use of a capacitive probe with a sampling frequency of 1 MHz, frequency response from∼4 Hz to ∼400 kHz, ampli-tude resolution of ∼35 µV, and timing accuracy of ∼12 ns. Numerical simulations of relativistic electron beams are performed with the transient, multimaterial, compress-5

ible, fluid dynamics code CAVEAT which was adapted to solve the electromagnetic equations and their effect on the electron and ion populations in a self-consistent way on the Los Alamos National Laboratory supercomputer facility. The Finite-Diff erence-Time-Domain (FDTD) method dynamically solves Maxwell’s equations on a spatial grid using equivalent vertical current sources representing the relativistic electron beam and 10

the causative lightning discharge and propagates the full wave radio electromagnetic fields to the wideband digital radio receiver.

Acknowledgements. This work was sponsored by the Natural Environment Research Council

(NERC) under grant NE/H024921/1 and the Science and Technology Facilities Council (STFC) under grant PP/E0011483/1. V.P.P. was supported by Aeronomy and Physical and Dynamical

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Meteorology Programs of the US National Science Foundation. The International Space Sci-ence Institute (ISSI) kindly supported and hosted the Coupling of Atmospheric Regions with Near-Earth Space (CARNES) team meetings which stimulated this work.

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Table 1.Observations of several electron beams associated with sprite occurrences. The date, time, and location of the causative lightning discharges are reported by the French lightning de-tection system M ´et ´eorage. The distances between the lightning discharges and the wideband

digital radio receiver in South-West England vary between∼490–1060 km. The

electromag-netic radiation bursts from the lightning discharge and the consecutive electron beam exhibit

time delays from∼2–9 ms. The time delays between the direct wave and the sky wave from the

electron beam can only be determined for distances up to∼500 km as a result of the larger

sig-nal to noise ratio of the electromagnetic recordings. The observed time delays from∼25–92 µs

indicate that all the electron beams are located at heights between∼16–72 km, well above the

top of the thundercloud at∼12 km (Fig. 1).

date time/UTC location lightning/receiver lightning/beam direct/sky wave height distance/km delay/ms delay/ µs km

31.08.2008 01:52:59.524482 0.4767◦_{E, 46.5408}◦_N ₅₇₁ _4.5/8.9 _59/25 _41/72

31.08.2008 02:18:26.265226 0.5489◦_{E, 46.8654}◦_N ₅₄₀ _8.0 ₉₂ ₁₆

31.08.2008 02:42:20.621219 0.3618◦_{E, 47.3155}◦_N ₄₈₉ _2.5 ₇₅ ₂₂

24.08.2009 21:04:24.032714 2.0992◦_{E, 43.6166}◦_N ₉₂₀ _2.0 _– _–

24.08.2009 21:18:11.336514 1.8931◦_{E, 43.8959}◦_N ₈₈₆ _7.0 _– _–

02.09.2009 02:09:56.601840 3.5730◦_{E, 42.8089}◦_N ₁₀₄₈ _5.5 _– _–

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Fig. 1. A meso-scale convective system is located over France and reaches an area of

∼400×400 km2at 01:45 UTC on 31.08.2008 as inferred from the cloud top infrared brightness

temperature. Many negative lightning discharges (circles) cluster in the∼12 km (Tmin=−64 C◦)

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Fig. 2. The main body of the sprite extends upwards from∼60–85 km height and the tendrils

of the sprite extend downwards from∼60–50 km as triangulated by use of two video cameras

from Pic du Midi in the French Pyr én ées (42.9◦_{N, 0.1}◦_{E) and Sant Vicenç de Castellet in}

North-Eastern Spain (41.7◦_{N, 1.9}◦_{E). The sprite body is surrounded by three columniform sprites}

at distances up to ∼20 km. The panels on the top and right hand side indicate the relative

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−100 −5 0 5 10 15

50 100 150

count

photometer

−10 −5 0 5 10 15

−100 0 100

[ E ] = mV/m

5 − 16 kHz

−10 −5 0 5 10 15

−200 0

200 40 − 400 kHz

[ t ] = ms

[ E ] = mV/m

sprite

lightning

lightning electron beams

Fig. 3.The sprite luminosity occurs∼3–6 ms after the causative positive lightning discharge at

0 ms (upper panel) as observed from Pic du Midi with a high-speed photometer. The lightning

discharge emits a burst of electromagnetic radiation in the frequency range from∼5–16 kHz

(middle panel) which is recorded with a wideband digital radio receiver in South-West England

(51.3◦_{N, 2.3}◦_{W). Two consecutive bursts of electromagnetic radiation in the frequency range}

∼40–400 kHz occur at∼4.4 ms and∼8.9 ms (bottom panel). These bursts are thought to be

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50 100 150 200 250 300 350 400 10−6

10−5 10−4 10−3

10−2

[ f ] = kHz

[ E ] = Vm

−1

Hz

−1/2

measured lightning measured electron beam background reference

50 100 150 200 250 300 350 400 10−6

10−5

10−4 10−3

10−2

[ f ] = kHz

[ E ] = Vm

−1

Hz

−1/2

simulated lightning simulated electron beam sensitivity limit

Fig. 4. The average spectra of electron beams (red lines) and their causative lightning

dis-charges (blue lines) on the left compare well with the theoretical simulations on the right.Left:

The average spectrum of the seven measured electron beams (Table 1) is relatively flat at

frequencies<40 kHz (red line) when compared with the average spectrum of their causative

lightning discharges (blue line). The lightning and electron beam spectra are∼1–2 orders of

magnitude larger than the average background spectrum (black line) which is recorded 10 ms

prior to the causative lightning discharges for reference. Right: The simulated electron beam

spectrum is relatively flat at frequencies <40 kHz (red line) when compared with the

simu-lated spectrum of the causative lightning discharge (blue line). The simusimu-lated spectra are

∼2–3 orders of magnitude larger than the sensitivity limit of the wideband digital radio receiver

∼1–2 µVm−1Hz−1/2which is inferred from time intervals without any bursts of electromagnetic

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−400 −200 0 200 400

[ E ] = mV/m

−150 −100 −50 0 50 100 150 200 250

−200 −100 0 100 200

[ t ] = µs

[ E ] = mV/m

lightning

electron beam

102 µs sky wave ground wave

59 µs sky wave direct wave

Fig. 5.The burst of electromagnetic radiation from the lightning discharge is composed of two

consecutive pulses which are delayed by∼102 µs (upper panel). The first pulse results from the

electromagnetic wave which propagates along the surface of the Earth to the receiver (ground wave). The second pulse results from the electromagnetic wave which is reflected from the ionosphere (sky wave). The burst of electromagnetic radiation from the electron beam is also

composed of two consecutive pulses (lower panel). The short time delay of∼59 µs indicates

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20 40 60 80 100

[ h ] = km

ionosphere

lightning receiver

ground wave

∆ t = 102 µs sky wave

0 100 200 300 400 500 600

20 40 60 80 100

[ d ] = km

[ h ] = km

ionosphere

lightning electron beam

receiver direct wave

∆ t = 59 µs sky wave sprite

Fig. 6.The time delay of∼102 µs between the ground wave and the sky wave from the lightning

discharge indicates that the reflecting ionosphere is located at a height of∼90 km (upper panel).

The time delay of∼59 µs between the direct wave and the sky wave from the electron beam

indicates that the electron beam is located at a height of∼41 km (lower panel). The electron